Horizon Distance Calculator - Calculator Academy

Enter your height above sea level, typically your eye level, into the calculator to determine the distance to the horizon.

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How the Horizon Distance Calculator Works

The horizon distance is the maximum geometric distance from your eye position to the point where the Earth’s curvature hides the surface. This calculator estimates that distance from your eye height, making it useful for boating, coastal viewing, photography, surveying, observation decks, and understanding how elevation changes visibility.

Core Formula

The exact geometry uses the Earth’s radius and your height above the surface:

d = \sqrt{2Rh + h^2}

For normal viewing heights, your height is tiny compared with the Earth’s radius, so the expression simplifies to:

d \approx \sqrt{2Rh}

That produces the practical forms most people use:

d_{mi} = 1.22459\sqrt{h_{ft}}

d_{km} \approx 3.57\sqrt{h_m}

d = distance to the horizon
R = Earth’s radius
h = eye height above the observed surface

What Height Should You Enter?

Use your total eye height above the surface you are viewing across. If you are standing on a cliff, bridge, tower, ship deck, or rooftop, include that elevation plus your eye level. For example, if you are on a 50 ft bluff and your eyes are about 6 ft above the ground, enter roughly 56 ft.

How to Use the Calculator

Measure or estimate your eye height.
Enter the value in feet, meters, centimeters, or inches.
Read the estimated horizon distance in miles, kilometers, meters, or feet.
If you want to know whether you can see another elevated object, add that object’s own horizon distance to yours.

When the Distant Object Also Has Height

If both the observer and the target rise above the surface, the maximum line-of-sight range is approximately the sum of both horizon distances:

d_{total,mi} \approx 1.22459\left(\sqrt{h_{1,ft}} + \sqrt{h_{2,ft}}\right)

This is especially helpful for ships, lighthouses, antennas, mountain peaks, offshore platforms, and tall buildings.

Quick Reference Values

Eye Height	Approx. Horizon Distance
6 ft (1.8 m)	3.0 mi (4.8 km)
30 ft (9.1 m)	6.7 mi (10.8 km)
100 ft (30.5 m)	12.2 mi (19.7 km)
500 ft (152.4 m)	27.4 mi (44.1 km)

Important Assumptions

The calculation assumes an unobstructed view over a curved Earth.
It estimates the geometric horizon, not guaranteed recognition distance of a target.
Terrain, trees, buildings, waves, haze, and lighting can reduce what you actually see.
Atmospheric refraction can sometimes let you see slightly farther than the basic geometric estimate.

Why Height Helps So Much

Horizon distance increases with the square root of height, which means visibility improves steadily but not linearly. Raising your viewpoint helps a lot, but doubling the visible distance requires much more than doubling your height.

Common Questions

Is this the same as distance across flat ground?: No. Horizon distance is limited by Earth curvature, not just by straight-line ground distance.
Should I enter eye height or elevation above sea level?: Use the height of your eyes above the surface you are viewing over. If you are above the water or ground on a structure or natural feature, include that extra elevation.
Why can I sometimes see a tall object even when its base is hidden?: The top of the object may still rise above the horizon. That is why combining observer height and target height gives a more realistic visibility range.
Does this calculator work only on Earth?: The built-in constant is for Earth. A different planetary radius would produce a different horizon distance.